My current assumption would be that it pulls this from either your dashboard (recent one), your itch profile page (recent one), or your creator page (recent one).
Now the issue is that you cannot really change any of those in terms of order, except for the last one, your creator page (where you can also decide to display collections). You said you already tried around with those collections, but did you also try to re-arrange the order your projects at the top (so those without an actual "collection") are displayed? You can hide and re-arrange your own projects specifically by selecting "Change Theme" at the top left and look under "My Projects" in the appearing sidebar. Best case scenario, by setting the project you want to show in your profile-link to be the first one (so the most top left), it will also influence the thumbnail for your link.
If that doesn't work, I am afraid I'm not sure if you can really have much of an influence on that within itch.io's current system.